So I already mentioned that everything has a matter-wave associated with it. Developing the idea a bit further, we get the concept of a wavefunction which, by convention, is denoted by .
Each physical system is described by a state function which determines all can be known about the system. … The wavefunction has to be finite and single valued throughout position space, and furthermore, it must also be a continuous and continuously differentiable function.
Furthermore, a wavefunction is generally a complex function i.e it consists of both a real part and an imaginary part.
- – A wavefunction
To get the probably of a particle being at a position , you have to get a real value out of the complex wavefunction. Hence the probably of finding a particle described by a wavefunction is the product of the function at and its complex conjugate at .
- – probability of finding the particle at .
To get the probability from a range where is a continous variable, you can take the integral of from to :